A227679 T(n,k)=Number of nXk 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(k+1) binary array having an odd sum, with rows and columns of the latter in lexicographically nondecreasing order

2, 4, 4, 7, 16, 7, 11, 50, 50, 11, 16, 131, 283, 131, 16, 22, 301, 1343, 1343, 301, 22, 29, 625, 5434, 11971, 5434, 625, 29, 37, 1198, 19188, 90884, 90884, 19188, 1198, 37, 46, 2153, 60484, 592791, 1330361, 592791, 60484, 2153, 46, 56, 3670, 173433, 3380440

Offset

1,1

Comments

Table starts

..2....4......7.......11..........16............22..............29

..4...16.....50......131.........301...........625............1198

..7...50....283.....1343........5434.........19188...........60484

.11..131...1343....11971.......90884........592791.........3380440

.16..301...5434....90884.....1330361......16795263.......184000783

.22..625..19188...592791....16795263.....418147052......9062032214

.29.1198..60484..3380440...184000783....9062032214....392636087774

.37.2153.173433.17161921..1773503344..172087530120..14928759496120

.46.3670.459198.78807477.15261176700.2897975481614.502146361367093

Links

R. H. Hardin, Table of n, a(n) for n = 1..144

Formula

Empirical for column k:

k=1: a(n) = (1/2)*n^2 + (1/2)*n + 1

k=2: [polynomial of degree 6]

k=3: [polynomial of degree 14]

k=4: [polynomial of degree 30]

k=5: [polynomial of degree 62]

Example

Some solutions for n=4 k=4
..0..1..0..1....0..0..0..0....0..0..0..0....0..0..0..1....1..0..1..0
..1..1..0..0....0..0..1..1....0..0..1..1....0..0..1..0....1..0..1..0
..0..1..1..1....0..0..0..0....0..1..0..1....0..1..0..1....0..0..1..0
..1..0..0..1....1..0..0..1....0..1..1..1....1..1..1..0....0..1..1..0

Crossrefs

Column 1 is A000124

Sequence in context: A223644 A223637 A223620 * A223782 A223716 A188607

Adjacent sequences: A227676 A227677 A227678 * A227680 A227681 A227682

Keyword

nonn,tabl

Author

R. H. Hardin Jul 19 2013

Status

approved